Algorithms for the Solution of Optimization Problems

Abstract

For generating solutions to vector optimization problems via algorithms based on a scalarization, the monotonicity properties of the scalarizing functionals are important. In this chapter, we present Benson’s Outer Approximation Algorithm that uses a scalarization by means of translation invariant functionals. Furthermore, we present proximal-point algorithms as well as an adaptive algorithm for solving vector optimization problems where translation invariant functionals are involved. We show that a scalarization by means of translation invariant functionals is useful for deriving an algorithm for solving set-valued optimization problems. Finally, we derive algorithms for solving vector optimization problems with variable domination structure using an extension of translation invariant functionals.